Magnonic holographic memory and methods

ABSTRACT

An electronic device using an array of magnetic wave guides is shown. In one example a memory device is shown that utilizes spin waves and a magnet storage element that interacts with the spin waves. In one example, an electronic device is shown that utilizes both a complementary metal oxide device and a magnonic device coupled together.

CLAIM OF PRIORITY

This application is a continuation of and claims the benefit of priority under 35 U.S.C. §120 to U.S. patent application Ser. No. 14/924,575, filed on Oct. 27, 2015, which claims the benefit priority under 35 U.S.C. §119(e) to U.S. Provisional Patent Application No. 62/069,617, filed Oct. 28, 2014, each which is incorporated herein by reference in its entirety.

TECHNICAL FIELD

This invention relates to computer memory and associated methods. Specific examples include magnonic holographic memory devices.

BACKGROUND

Existing computer memory devices, such as CMOS memory devices can be challenged in selected operations, such as image processing, speech recognition, etc. Improved memory devices are desired with improved characteristics such as increased speed and reduced power consumption.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a mangnonic device according to an example of the invention.

FIG. 2 shows a schematic of a mangnonic device according to an example of the invention.

FIG. 3 shows a four arm example of a mangnonic device according to an example of the invention.

FIG. 4 shows another four arm example mangnonic device according to an example of the invention.

FIG. 5 shows a double cross example of a mangnonic device according to an example of the invention.

FIG. 6 shows experimental operating data of a mangnonic device according to an example of the invention.

FIG. 7 shows additional experimental operating data of a mangnonic device according to an example of the invention.

FIG. 8 shows another double cross example of a mangnonic device according to an example of the invention.

FIG. 9 shows one method according to an example of the invention.

FIG. 10 shows an electronic device incorporating a magnonic device according to an example of the invention.

DETAILED DESCRIPTION

In the following detailed description, reference is made to the accompanying drawings which form a part hereof, and in which is shown, by way of illustration, specific embodiments in which the invention may be practiced. In the drawings, like numerals describe substantially similar components throughout the several views. These embodiments are described in sufficient detail to enable those skilled in the art to practice the invention. Other embodiments may be utilized and structural, or logical changes, etc. may be made without departing from the scope of the present invention.

In this work, we present recent developments in magnonic holographic memory devices exploiting spin waves for information transfer. Example devices comprise a magnetic matrix and spin wave generating/detecting elements placed on the edges of the waveguides. The matrix consists of a grid of magnetic waveguides connected via cross junctions. Magnetic memory elements are incorporated within the junction while the read-in and read-out is accomplished by the spin waves propagating through the waveguides. We present experimental data on spin wave propagation through NiFe and YIG magnetic crosses. The obtained experimental data show prominent spin wave signal modulation (up to 20 dB for NiFe and 35 dB for YIG) by the external magnetic field, where both the strength and the direction of the magnetic field define the transport between the cross arms. We also present experimental data on the 2-bit magnonic holographic memory built on the double cross YIG structure with micro-magnets placed on the top of each cross. It is possible to recognize the state of each magnet via the interference pattern produced by the spin waves with all experiments done at room temperature. Magnonic holographic devices aim to combine the advantages of magnetic data storage with wave-based information transfer. We present estimates on the spin wave holographic devices performance, including power consumption and functional throughput. According to the estimates, magnonic holographic devices may provide data processing rates higher than 1×10¹⁸ bits/cm²/s while consuming 0.15 mW. Technological challenges and fundamental physical limits of this approach are also discussed.

I. Introduction

There is growing interest in novel computational devices able to overcome the limits of the current complimentary-metal-oxide-semiconductor (CMOS) technology and provide further increase of the computational throughput. A number of the “beyond CMOS” proposals are aimed at the development of new switching technologies with increased scalability and improved power consumption characteristics over the silicon transistor. However, it is difficult to expect that a new switch will outperform CMOS in all figures of merit, and more importantly, will be able to provide multiple generations of improvement as was the case for CMOS. An alternative route to the computational power enhancement is via the development of novel computing devices, aimed not to replace, but to complement CMOS by special task data processing. Spin wave (magnonic) logic devices take the advantages of the wave interference at nanometer scale and utilize phase in addition to amplitude for building logic units for parallel data processing.

A spin wave is a collective oscillation of spins in a magnetic lattice, analogous to phonons, the collective oscillation of the nuclear lattice. The typical propagation speed of spin waves does not exceed 10 cm/s, while the attenuation time at room temperature is about a nanosecond in the conducting ferromagnetic materials (e.g. NiFe, CoFe) and may be hundreds of nanoseconds in non-conducting materials (e.g. YIG). Such a short attenuation time explains the lack of interest in spin waves as a potential information carrier in the past. The situation has changed drastically as the technology of integrated logic circuits has scaled down to the deep sub-micrometer scale, where the short propagation distance of spin waves (e.g. tens of microns at room temperature) is more than sufficient for building logic circuits. At the same time, spin waves have several inherent appealing properties making them promising for building wave-based logic devices. For instance, spin wave propagation can be directed by using magnetic waveguides similar to optical waveguides. The amplitude and the phase of propagating spin waves can be modulated by an external magnetic field. Spin waves can be generated and detected by electronic components (e.g. multiferroics), which make them suitable for integration with conventional logic circuits. Finally, the coherence length of spin waves at room temperature may exceed tens of microns, which allows for the utilization of spin wave interference for logic functionality. Such a long coherence length at room temperature is a result of the collective nature of spin wave phenomena, where a large number of spins precessing together are united by strong exchange coupling. It makes spin waves much more prone to scattering than a single electron and resolves one of the most difficult problems of spintronics associated with the necessity to preserve spin orientation while transmitting information between the spin-based units.

With zero applied current, the spin waves in two branches interfere constructively and propagate through the structure. The waves interfere destructively and do not propagate through the structure if a certain electric current is applied. At some point, magnonic logic devices resemble the classical field effect transistor, where the magnetic field produced by the electric current modulates the propagation of the spin wave—an analog to the electric current. Spin waves can be combined with nano-magnetic logic to combine the advantages of non-volatile data storage in magnetic memory and the enhanced functionality provided by the spin wave buses. The use of spin wave interference makes it possible to realize Majority gates (which can be used as AND or OR gates) and NOT gates with a fewer number of elements than is required for transistor-based circuitry, promising the further reduction of the size of the logic gates. In one example three-input spin wave Majority gates are realized. However, the integration of the spin wave buses with nano-magnets in a digital circuit, where the magnetization state of the nano-magnet is controlled by a spin wave has not yet been realized until this disclosure.

An alternative approach to spin wave-based logic devices is to build non-Boolean logic gates for special task data processing. The essence of this approach is to maximize the advantage of spin wave interference. Wave-based analog logic circuits are potentially promising for solving problems requiring parallel operation on a number of bits at time (i.e. image processing, image recognition). The concept of magnonic holographic memory (MHM) for data storage and special task data processing has been recently proposed. Holographic devices for data processing have been extensively developed in optics during the past five decades. The development of spin wave-based devices allows us to implement some of the concepts developed for optical computing to magnetic nanostructures utilizing spin waves instead of optical beams. There are certain technological advantages that make the spin wave approach even more promising than optical computing. First, short operating wavelength (i.e. 100 nm and below) of spin wave devices promises a significant increase of the data storage density (˜λ² for 2D and ˜λ³ for 3D memory matrixes). Second, even more importantly, is that spin wave bases devices can have voltage as an input and voltage as an output, which makes them compatible with the conventional CMOS circuitry. Though spin waves are much slower than photons, magnonic holographic devices may possess a higher memory capacity due to the shorter operational wavelength and can be more suitable for integration with the conventional electronic circuits.

The present disclosure shows recent experimental results on magnonic holographic memory and discuss the advantages and potential shortcomings of this approach. The rest of the paper is organized as follows. In Section II, we describe the structure and the principle of operation of magnonic holographic memory. Next, we present experimental data on the first 2-bit magnonic holographic memory in Section III. The advantages and the challenges of the magnonic holographic devices are discussed in the Sections IV. In Section V, we present the estimates on the practically achievable performance characteristics.

One example of a method of operating a memory or logic device is shown in FIG. 9. In operation 902, a holographic data point is formed using spin wave interactions in a device. In operation 904, the data point is stored in the device. In operation 906, and the data point is subsequently read.

II. Material Structure and the Principle of Operation

The schematics of a MHM device are shown in FIG. 1(A). The core of the structure is a magnetic matrix consisting of the grid of magnetic waveguides with nano-magnets placed on top of the waveguide junctions. Without loss of generality, we have depicted a 2D mesh of orthogonal magnetic waveguides, though the matrix may be realized as a 3D structure comprising the layers of magnetic waveguides of a different topology (e.g. honeycomb magnetic lattice). The waveguides serve as a media for spin wave propagation—spin wave buses. The buses can be made of a magnetic material such as yttrium iron garnet Y3Fe₂(FeO4)₃ (YIG) or permalloy (Ni₈₁Fe₁₉) ensuring maximum possible group velocity and minimum attenuation for the propagating spin waves at room temperature. The nano-magnets placed on top of the waveguide junctions act as memory elements holding information encoded in the magnetization state. The nano-magnet can be designed to have two or several thermally stable states of magnetization, where the number of states defines the number of logic bits stored in each junction. The spins of the nano-magnet are coupled to the spins of the junction magnetic wires via the exchange and/or dipole-dipole coupling affecting the phase of the propagation of spin waves. The phase change received by the spin wave depends on the strength and direction of the magnetic field produced by the nano-magnet. At the same time, the spins of the nano-magnet are affected by the local magnetization change caused by the propagating spin waves.

The input/output ports are located at the edges of the waveguides. These elements are aimed to convert the input electric signals into spin waves, and vice versa, convert the output spin waves into electrical signals. There are several possible options for building such elements by using micro-antennas spin torque oscillators, and multiferroic elements.

For example, the micro-antenna is a conducting contour placed in the vicinity of the spin wave bus. An electric current passed through the contour generates a magnetic field around the current-carrying wires, which excites spin waves in the magnetic material, and vice versa, a propagating spin wave changes the magnetic flux from the magnetic waveguide and generates an inductive voltage in the antenna contour. The advantages and shortcomings of different input/output elements will be discussed later in the text.

Spin waves generated by the edge elements are used for information read-in and read-out. The difference among these two modes of operation is in the amplitude of the generated spin waves. In the read-in mode, the elements generate spin waves of a relatively large amplitude, so two or several spin waves coming in-phase to a certain junction produce magnetic field sufficient for magnetization change within the nano-magnet. In the read-out mode, the amplitude of the generated spin waves is much lower than the threshold value required to overcome the energy barrier between the states of nano-magnets. So, the magnetization of the junction remains constant in the read-out mode.

The formation of the hologram occurs in the following way. The incident spin wave beam is produced by the number of spin wave generating elements (e.g. by the elements on the left side of the matrix as illustrated in FIG. 1(B)). All the elements are biased by the same RF generator exciting spin waves of the same frequency, f, and amplitude, A₀, while the phase of the generated waves are controlled by DC voltages applied individually to each element. Thus, the elements constitute a phased array allowing us to artificially change the angle of illumination by providing a phase shift between the input waves. Propagating through the junction, spin waves accumulate an additional phase shift, Δφ, which depends on the strength and the direction of the local magnetic field provided by the nano-magnet, H_(m):

$\begin{matrix} {{{\Delta\varphi} = {\int_{0}^{r}{{k\left( {\overset{\rightharpoonup}{H}}_{m} \right)}{dr}}}},} & (1) \end{matrix}$

where the particular form of the wavenumber k(H) dependence varies for magnetic materials, film dimensions, the mutual direction of wave propagation and the external magnetic field. For example, spin waves propagating perpendicular to the external magnetic field (magnetostatic surface spin wave—MSSW) and spin waves propagating parallel to the direction of the external field (backward volume magnetostatic spin wave—BVMSW) may obtain significantly different phase shifts for the same field strength. The phase shift Δφ produced by the external magnetic field variation δH in the ferromagnetic film can be expressed as follows:

$\begin{matrix} {{\frac{\Delta\varphi}{\partial H} = {\frac{l}{d}\frac{\left( {\gamma \; H} \right)^{2} + \omega^{2}}{2{\pi\gamma}^{2}M_{S}H^{2}}({BVMSW})}},{\frac{\Delta\varphi}{\partial H} = {{- \frac{l}{d}}\frac{\gamma^{2}\left( {H + {2\pi \; M_{S}}} \right)}{\omega^{2} - {\gamma^{2}{H\left( {H + {4\pi \; M_{S}}} \right)}}}\left\{ {MSSW} \right)}},} & (2) \end{matrix}$

where Δφ is the phase shift produced by the change of the external magnetic field δH, I is the propagation length, d is the thickness of the ferromagnetic film, γ is gyromagnetic ratio, ω=2πf, 4πM_(s) is the saturation magnetization of the ferromagnetic film. The output signal is a result of superposition of all the excited spin waves traveling through the different paths of the matrix. The amplitude of the output spin wave is detected by the voltage generated in the output element (e.g. the inductive voltage produced by the spin waves in the antenna contour). The amplitude of the output voltage is corresponding to the maximum when all the waves are coming in-phase (constructive interference), and the minimum when the waves cancel each other (destructive interference). The output voltage at each port depends on the magnetic states of the nano-magnets within the matrix and the initial phases of the input spin waves. In order to recognize the internal state of the magnonic memory, the initial phases are varied (e.g. from 0 to π). The ensemble of the output values obtained at the different phase combinations constitute a hologram which uniquely corresponds to the internal structure of the matrix.

In general, each of the nanomagnets can have more than 2 thermally stable states, which makes it possible to build a multi-state holographic memory device (i.e. z^(N) possible memory states, where z is the number of stable magnetic states of a single junction and N is the number of junctions in the magnetic matrix). The practically achievable memory capacity depends on many factors including the operational wavelength, coherence length, the strength of nano-magnets coupling with the spin wave buses, and noise immunity. In the next Section, we present experimental data on the operation of the prototype 2-bit magnonic holographic memory.

III. Experimental Data

The set of experiments started with the spin wave transport study in a single cross structure, which is the elementary building block for 2D MHM as depicted in FIG. 1. In FIG. 1, an example array 100 of intersecting magnetic wave guides 102 is shown. A number of magnets 104 are shown located at junctions of the intersecting magnetic wave guides 102. Also shown in FIG. 1, are a number of spin wave generator/detectors 106.

Two types of single cross devices made of Y₃Fe₂(FeO₄)₃(YIG) and Permalloy (Ni₈₁Fe₁₉) were fabricated. Both of these materials are promising for application in magnonic waveguides due to their high coherence length of spin waves. At the same time, YIG and Permalloy differ significantly in electrical properties (e.g. YIG is an insulator, permalloy is a conductor) and in fabrication method. YIG cross structures 110 were made from single crystal YIG films epitaxially grown on top of Gadolinium Gallium Garnett (Gd₃Ga₅O₁₂) substrates using the liquid-phase transition process. After the films were grown, micro-patterning was done by laser ablation using a pulsed infrared laser (λ˜1.03 μm), with a pulse duration of ˜256 ns. The YIG cross junction has the following dimensions: the length of the whole structure is 3 mm; the width of the arm in 360 μm; thickness is 3.6 um. Permalloy crosses were fabricated on top of oxidized silicon wafers. The wafer was spin coated with a 5214E Photoresist at 4000 rpm and exposed using a Karl Suss Mask Aligner. After development, a permalloy metal film was deposited via Electron-Beam Evaporation with a thickness of 100 nm and with an intermediate seed layer of 10 nm of Titanium to increase the adhesion properties of the Permalloy film. Lift-off using acetone completed the process. Permalloy cross junction has the following dimensions: the length of the whole structure is 18 um; the width of the arm in 6 μm; thickness is 100 nm.

Spin waves in YIG and Permalloy structures were excited and detected via micro-antennas that were placed at the edges of the cross arms. Antennas were fabricated from gold wire and mechanically placed directly at the top of the YIG cross. In the case of permalloy, the conducting cross was insulated with a 100 nm layer of SiO₂ deposited via Plasma-Enhanced Chemical Vapor Deposition (PECVD) and gold antennas were fabricated using the same photolithographic and lift-off procedure as with the permalloy cross structures. A Hewlett-Packard 8720A Vector Network Analyzer (VNA) was used to excite/detect spin waves within the structures using RF frequencies. Spin waves were excited by the magnetic field generated by the AC electric current flowing through the antenna(s). The detection of the transmitted spin waves is via inductive voltage measurements. Propagating spin waves change the magnetic flux from the surface, which produces an inductive voltage in the antenna contour. The VNA allowed the S-Parameters of the system to be measured; showing both the amplitude of the signals as well as the phase of both the transmitted and reflected signals. Samples were tested inside a GMW 3472-70 Electromagnet system which allowed the biasing magnetic field to be varied from −1000 Oe to +1000 Oe. The schematics of the experimental setup for spin wave transport study in the single cross structures are shown in FIG. 2.

First, we studied spin wave propagation between the four arms of the permalloy cross-structure as shown in FIG. 3(A-B) under different bias magnetic field. The input/output ports are numbered from 1 to 4 starting at the 9 O'clock position and then enumerated sequentially in along a clockwise direction. In order to define the angle between the external magnetic field and the direction of signal propagation, we define the X axis along the line from port 1 to port 3, and the Y axis along the line from port 4 to port 2 propagating as depicted in FIG. 2. Spin waves were excited on port 2 (the top of the magnetic cross) and read out from port 4 (the bottom of the cross) (see FIG. 1). The graph in FIG. 3 shows the change of the amplitude of the transmitted signal as a function of the strength of the external magnetic field directed perpendicular to the propagating spin waves as depicted in the inset to FIG. 3. Hereafter, we show the relative change of the amplitude in decibels normalized to some value (e.g. to the maximum value). The normalization is needed as the input power varies significantly for permalloy and YIG structures as well as for the type of experiment. The reference transmission level is taken at 300 Oe, where the S₁₂ parameter is at its absolute maximum. At small magnetic fields below 100 Oe a very small amplitude signal was observed. At approximately 150 Oe there is a noticeable increase in the amplitude followed by a plateau in the response as the field is increased to 500 Oe. Also of interest is the response of the signal as a function of the applied magnetic field direction. In FIG. 3(D), we present an example of the experimental data showing the influence of the direction of the bias field on spin waves transport from port 2 to port 4. The results demonstrate prominent change in the amplitude of the transmitted signal [18 dB] when the field is applied between 20° and 30°. The main observations of these experiments are the following. (i) Spin wave propagation through the cross junction can be efficiently controlled by the external magnetic field. (ii) Both the amplitude and the direction of the magnetic field can be utilized for spin wave control.

We conducted similar experiments on the YIG single cross device as shown in FIG. 4. It was observed that prominent signal modulation could be determined by the direction and the strength of the external magnetic field. In FIG. 4, there is shown an example of experimental data on the spin wave transport between ports 2 and 1. The maximum transmission between the orthogonal arms occurs when the field is applied at 68°, while the minimum is seen when the field is applied at 0°. The On/Off ratio for the YIG cross reaches 35 dB. Of noticeable interest is also the effect of non-reciprocal spin wave propagation. The two curves in FIG. 4(D) show signal propagation from port 2 to port 4, and in the opposite direction from port 4 to port 2. The measurements are done at the same bias magnetic field of 998 Oe. There is a difference of about 5 dB for the signals propagating in the opposite direction. The effect is observed in a relatively narrow frequency range (e.g. from 5.2 GHz to 5.4 GHz). Concluding on the spin wave transport in the permalloy and YIG single cross structures, prominent signal modulation has been observed in both cases. For the chosen parameters, the operation frequency is slightly higher for YIG structure (˜5 GHz) than for permalloy (˜3 GHz). The speed of signal propagation is slightly faster in permalloy (3.5×106 cm/s) than in YIG (3.0×106 cm/s). The difference in the spin wave transport can be attributed to the differences between the intrinsic material properties of YIG and Permalloy as well as the difference in the cross dimensions. It is important to note, that in both cases the level of the power consumption was at the microwatt scale (e.g. 0.1 μW-1.0 μW for permalloy and 0.5 μW-5.0 μW for YIG) with no feasible effect of micro heating on the spin wave transport. The summary of the experimental findings for permalloy and YIG single cross junctions cab be found in Table I.

TABLE I Permalloy YIG Cross dimensions L = 18 μm, w = 6 μm, L = 3 mm, w = 300 μm, d = 100 nm d = 3.8 μm Operational Frequency 3 GHz-4 GHz 5 GHz-6 GHz SW group velocity 3.5 × 10⁶ cm/s 3.0 × 10⁶ cm/s Maximum On/Off 20 dB 35 dB ratio Power consumption 0.1 μW-1 μW 0.5 μW-5 μW Compatibility with Yes No Silicon

Next, we carried out experiments on spin wave transport and interference in the double-cross structure 500 made of YIG as shown in FIG. 5. The choice of material is mainly due to the larger size of the structure and spin wave detecting antennas, where the larger the area of the detecting contour results in higher the observed output inductive voltage. The multi-port double-cross YIG structure is suitable for the study of spin wave interference. In this study, several coherent spin wave signals were excited by ports 3, 4, 5 and 6 connected to one port of the VNA. The output is detected at port 1. The phase shifters were employed to vary the phase difference between the ports as shown in FIG. 5(B).

FIG. 6 show the experimental data on the output voltage collected in the frequency range from 5.3 GHz to 5.5 GHz. The curves of the different color correspond to the different phase shifts between the spin wave generated ports. Phase 1 represents a change in the phase of ports 4 and 6 and Phase 2 represents a change in the phase of ports 3 and 5. FIGS. 6(B-D) show the slices of data taken at a frequency of 5.385 GHz, 5.410 GHz and 5.45 GHz, respectively. The black markers denoted by squares depict the experimentally obtained data, and the red markers denoted by circles depict the theoretical output for the ideal case of the interfering waves of the same frequency and amplitude. The theoretical data is normalized to have the same maximum value as the experimental data at phase difference zero (constructive interference). Experimental data shows an excellent fit with the theoretical predictions, which implies the dominant role of wave interference in the output signal formation. Discrepancies in the amplitude can be attributed to parasitic noise which raises the base amplitude of the signal to greater than nonzero value even when the phase should be perfectly destructive.

The data presented in FIG. 7 are collected in the experiments where Phase 2 (ports 3 and 5) was changed, while Phase 1 (ports 2 and 4) was kept constant. The ability to independently change the initial phases of the spin waves is equivalent to changing the angle of illumination for building a holograms as illustrated in FIG. 1(B). In FIG. 7, we present experimental data showing the holographic image of the double-cross structure without memory elements. The surface is a computer reconstructed 3-D plot showing the output voltage as a function of Phase 1 and Phase 2. The excitation frequency is 5.40 GHz, the bias magnetic field is 1000 Oe. In this case, antennas on ports 2 and 4 generated spin waves with the initial Phase 1, and antennas on ports 3 and 5 generated spin waves with initial Phase 2. No signal is applied to port 1. The output is detected at port 6. The change of the output inductive voltage is a result of spin wave interference. It has maximum values in the case of the constructive interference (i.e. Phase 1=Phase 2, (0,0) or (π,π)), and shows minimum output signal when the waves are coming out-of-phase ((0,π) or (π,0)).

Finally, we conducted experiments to demonstrate the operation of a prototype 2-bit magnonic holographic memory device. Two micro-magnets made of cobalt magnetic film were placed on top of the junctions of the double-cross YIG structure. As mentioned in Section II, these magnets serve as a memory element, where the magnetic state represents logic zeroes and ones. The schematic of the double-cross structure with micro-magnets attached are shown in FIG. 8(A). The length of each magnet is 1.1 mm, the width is 360 μm and each has a coercivity of 200-500 Oersted (Oe). For the test experiments, we used four mutual orientations of micro-magnets, where the magnets are oriented parallel to the axis connecting ports 1-6, or the axis connecting 2-4; and two cases when the micro-magnets are oriented in the orthogonal directions. Holographic images were collected for each case. FIG. 8 shows the collection of data corresponding to output voltage obtained for different magnetic configurations. The phases of the input elements are the same as in the previous experiment. Markers of different shape and color in the legend of FIG. 8 represent the direction of the “north” end of the micro magnet. The output from the same structure varies significantly for different phase combinations. In some cases, the magnetic states of the magnets can be recognized by just one measurement (e.g. (0,0) phase combination). It is also possible that different magnetic states provide almost the same output (e.g. parallel and orthogonal magnet configurations measured at (π,0) phase combination).

The main observation we want to emphasize is the feasibility of parallel read-out and reconstruction of the magnetic state via spin wave interference. As one can see from the data in FIG. 8(B), it is possible to distinctly identify the magnetic states by changing the phases of the interfering waves, which is similar to changing the angle of observation in a conventional optical hologram. We would like to emphasize that all experiments reported in this Section are done at room temperature.

IV. Discussion

The obtained experimental data show the practical feasibility of utilizing spin waves for building magnonic holographic logic devices and helps to illustrate the advantages and shortcomings of the spin wave approach. Of these results there are several important observations we wish to highlight.

First, spin wave interference patterns produced by multiple interfering waves are recognized for a relatively long distance (more than 3 millimeters between the excitation and detection ports) at room temperature. Coding information into the phase of the spin waves appears to be a robust instrument for information transfer showing a negligible effect to thermal noise and immunity to the structures imperfections. This immunity to the thermal fluctuations can be explained by taking into account that the flicker noise level in ferrite structures usually does not exceed −130 dBm. At the same time, spin waves are not sensitive to the structure's imperfections which have dimensions much shorter than the wavelength. These facts explain the good agreement between the experimental and theoretical data (e.g. as shown in FIG. 6).

Second, spin wave transport in the magnetic cross junctions is efficiently modulated by an external magnetic field. Spin wave propagation through the cross junction depends on the amplitude as well as the direction of the external field. This provides a variety of possibilities for building magnetic field-effect logic devices for general and special task data processing. Boolean logic gates such as AND, OR, NOT can be realized in a single cross structure, where an applying external field exceeding some threshold stops/allows spin wave propagation between the selected arms. The ability to modulate spin wave propagation by the direction of the magnetic field is useful for application in non-Boolean logic devices. It is important to note that in all cases the magnitude of the modulating magnetic field is of the order of hundreds of Oersteds, which can be produced by micro- and nano-magnets.

Finally, it appears possible to recognize the magnetic state of the magnet placed on the top of the cross junction via spin waves, which introduces an alternative mechanism for magnetic memory read out. This property itself may be utilized for improving the performance of conventional magnetic memory devices. However, the fundamental advantage of the magnonic holographic memory is the ability to read-out a number of magnetic bits in parallel though the obtained experimental data demonstrates the parallel read-out of just two magnetic bits. In the rest of this Section, we discuss the fundamental limits and the technological challenges of building multi-bit magnonic holographic devices and present the estimates on the device performance.

We start the discussion with the choice of magnetic material for building spin waveguides. There are two materials that have become predominant, permalloy (Ni₈₁Fe₁₉) and YIG, for spin wave devices prototyping. The coherence length of spin waves in permalloy is about tens of microns at room temperature while the coherence length in a non-conducting YIG exceeds millimeters. The attenuation time for spin waves at room temperature is about a nanosecond in permalloy and a hundreds of nanoseconds in YIG. However, the fabrication of YIG waveguides may require a special gadolinium gallium garnet (GGG) substrate. In contrast, a permalloy film can be deposited onto a silicon platform by using the sputtering technique. Though YIG has better properties in terms of the coherence length and a lower attenuation, permalloy is more convenient for making magnonic devices on a silicon substrate.

In order to make a multi-bit magnonic holographic devices, the operating wavelength should be scaled down below 100 nm. The main challenge with shortening the operating wavelength is associated with the building of nanometer-scale spin wave generating/detecting elements. There are several possible ways of building input/output elements by using micro-antennas, spin torque oscillators, and multi-ferroic elements. So far, micro-antennas are the most convenient and widely used tool for spin wave excitation and detection in ferromagnetic films. Reducing the size of the antenna will lead to the reduction of the detected inductive voltage. This fact limits the practical application of any types of conducting contours for spin wave detection. The utilization of spin torque oscillators makes it possible to scale down the size of the elementary input/output port to several nanometers. The main challenge for the spin torque oscillators approach is to reduce the current required for spin wave generation. More energetically efficient are the two-phase composite multiferroics comprising piezoelectric and magnetostrictive materials.

An electric field applied across the piezoelectric produces stress, which, in turn, affects the magnetization of the magnetoelastic material. The advantage of the multiferroic approach is that the magnetic field required for spin wave excitation is produced via magneto-electric coupling by applying an alternating electric field rather than an electric current. For example, in Ni/PMN-PT synthetic multiferroic, an electric field of 0.6 MV/m may be applied across the PMN-PT in order to produce 90 degree magnetization rotation in Nickel. Such a relatively low electric field required for magnetization rotation translates in ultra-low power consumption for spin wave excitation. At the same time, the dynamics of the synthetic multiferroics, especially at the nanometer scale, remains mostly unexplored.

To benchmark the performance of the magnonic holographic devices, we apply a charge-resistance approach. The details of the estimates and the key assumptions are given in Appendix A. According to the estimates, MHM device consisting of 32 inputs, with a 60 nm separation distance between the inputs would consume as low as 150 μW of power or 72 fJ per computation. At the same time, the functional throughput of the MHM scales proportional to the number of cells per area/volume and exceeds 1.5×10¹⁸ bits/cm²/s for a 60 nm feature size. It is interesting to note, that holographic logic units can be used for solving certain nondeterministic polynomial time (NP) class of problems (i.e. finding the period of the given function). The efficiency of holographic computing with classical waves is somewhere intermediate between digital logic and quantum computing, allowing us to solve a certain class of problems fundamentally more efficient than general-type processors but without the need for quantum entanglement. Image recognition and processing are among the most promising applications of magnonic holographic device exploiting its ability to process a large number of bits/pixels in parallel within a single core.

It may be expected that the amplitude/phase of the redirected (bended) spin wave depends on the wavelength/size ratio, the material properties of the cross, and magnetic field produced by the nano-magnet. We attribute the change in the interference pattern to the different phase shifts accumulated by spin waves propagating under the nano-magnets of different orientation (i.e. Eqs. 1-2).

CONCLUSIONS

The collected experimental data show rich physical phenomena associated with spin wave propagation in single- and double-cross structures. Prominent signal modulation by the direction, rather than the amplitude of magnetic field and the low effect of thermal noise on spin wave propagation at room temperature are among the many interesting findings presented here. The effect of spin wave redirection between the cross arms by the external magnetic field may be further exploited for building a variety of logic devices. Besides, spin waves appear to be a robust instrument allowing us to sense the magnetic state of micro-magnets by the change in the interference pattern. It is possible to recognize the unique holographic output for the different orientations of micro-magnets in a relatively long device at room temperature. Overall, the obtained data demonstrates building magnonic holographic devices. In one example, these holographic devices may be aimed not to replace but to complement CMOS in special type data processing such as speech recognition and image processing. According to estimates, scaled magnonic holographic devices may provide more than 1×10¹⁸ bits/cm²/s data processing rate while consuming less than 0.2 mW of energy. The development of scalable magnonic holographic devices and their incorporation with conventional electronic devices may pave the road to the next generations of logic devices with functional capabilities far beyond current CMOS.

FIG. 10 shows an example electronic device incorporating magnonic memory according to an embodiment of the invention. FIG. 10 shows a magnonic memory device 1002 and a complementary metal oxide device 1020. The magnonic memory device 1002 is coupled to the complementary metal oxide device 1020 with communication pathway 1012. In the example of FIG. 10, the magnonic memory device 1002 includes an array of intersecting magnetic wave guides 1004, and spin wave generator/detectors 1006, 1008 located at a periphery of the array 1004. The example of FIG. 10 further includes circuitry 1010 to covert electrical signals to spin waves and to convert spin waves to electrical signals.

To better illustrate the method and apparatuses disclosed herein, a non-limiting list of embodiments is provided here:

Example 1 includes a memory device, comprising an array of intersecting magnetic wave guides, a number of magnets located at junctions of the intersecting magnetic wave guides, and spin wave generator/detectors located at a periphery of the array and coupled to the intersecting magnetic wave guides.

Example 2 includes the memory device of example 1, further including circuitry to covert electrical signals to spin waves and to convert spin waves to electrical signals.

Example 3 includes the memory device of any one of examples 1-2, wherein the circuitry is configured to control both phase and amplitude of the spin waves.

Example 4 includes the memory device of any one of examples 1-3, wherein the array of intersecting magnetic wave guides includes a 2-dimensional array.

Example 5 includes the memory device of any one of examples 1-4, wherein the array of intersecting magnetic wave guides includes a 3-dimensional array.

Example 6 includes the memory device of any one of examples 1-5, wherein each magnet in the number of magnets is capable of two states.

Example 7 includes the memory device of any one of examples 1-6, wherein each magnet in the number of magnets is capable of more than two states.

Example 8 includes an electronic device, comprising a complementary metal oxide device and a magnonic memory device coupled to the complementary metal oxide device, the magnonic memory device including an array of intersecting magnetic wave guides, a number of magnets located at junctions of the intersecting magnetic wave guides, spin wave generator/detectors located at a periphery of the array and coupled to the intersecting magnetic wave guides, and circuitry to covert electrical signals to spin waves and to convert spin waves to electrical signals.

Example 9 includes the electronic device of example 8, wherein the CMOS device includes a processor.

Example 10 includes the electronic device of any one of examples 8-9, wherein the CMOS device includes a memory device.

Example 11 includes the electronic device of any one of examples 8-10, wherein the array of intersecting magnetic wave guides include yttrium iron garnet wave guides.

Example 12 includes the electronic device of any one of examples 8-11, wherein the array of intersecting magnetic wave guides include permalloy wave guides.

Example 13 includes the electronic device of any one of examples 8-12, wherein the permalloy wave guides are formed on silicon.

Example 14 includes the electronic device of any one of examples 8-13, wherein the spin wave generator/detectors include micro-antennae.

Example 15 includes the electronic device of any one of examples 8-14, wherein the spin wave generator/detectors include spin torque oscillators.

Example 16 includes the electronic device of any one of examples 8-15, wherein the spin wave generator/detectors include multiferrotic elements.

Example 17 includes a method, comprising forming a holographic data point using spin wave interactions in a device, storing the data point in the device, and reading the data point.

Example 18 includes the method of example 17, wherein storing the data point includes storing the data point in a magnet located at an intersection of magnetic wave guides in an array.

Example 19 includes the method of any one of examples 17-18, further including converting at least one electrical signal to a spin wave to store the data point.

Example 20 includes the method of one of examples 17-19, further including converting a spin wave to an electrical signal when reading the data point.

APPENDIX A

This section contains the details on the power consumption estimates. We assume that the input to each magnetoelectric (ME) cell is an AC voltage with amplitude created in a RLC oscillator. Then the power dissipation on resonance is

$\begin{matrix} {P_{i\; n} = {\frac{V_{i\; n}^{2}}{2R}.}} & (1) \end{matrix}$

The amplitude of the electric field in the piezoelectric of thickness t_(pz) is

E _(in) =V _(in) /t _(pz),  (2)

The amplitude of strain created in the piezoelectric of the ME cell is

∈_(xx) =d ₁₁ E _(in),  (3)

where the piezoelectric coefficient is d₃₁. Hereafter, it is assumed that spin wave is propagating along the X axis as shown in the inset to FIG. 2. The stress transferred to the ferromagnet is

σ=Y∈ _(xx),  (4)

where the Young's modulus of the piezoelectric is Y. The change in the magnetic anisotropy due to magnetostriction is

$\begin{matrix} {{U_{m\; s} = {\frac{3}{2}{\lambda\sigma}}},} & (5) \end{matrix}$

where the magnetostriction coefficient of the ferromagnet is λ. Then the maximum amplitude of magnetization change is

$\begin{matrix} {{{\Delta \; M_{x}} \approx \frac{2U_{m\; s}}{\mu_{0}M_{s}}},} & (6) \end{matrix}$

where the permeability of vacuum is μ₀, and the saturation magnetization is M_(s). This can be expressed via the magnetoelectric coefficient

$\begin{matrix} {\alpha \approx \frac{\mu_{0}\Delta \; M_{x}}{E_{i\; n}} \approx {\frac{3\lambda \; {Yd}_{31}}{M_{s}}.}} & (7) \end{matrix}$

Then the generated dimensionless amplitude of the spin wave can be approximated as follows

$\begin{matrix} {{A_{i\; n} = {\frac{\Delta \; M_{x}}{M_{s}} \approx \frac{\alpha \; V_{i\; n}}{\mu_{0}M_{s}t_{pz}}}},} & (8) \end{matrix}$

The spin waves interact and attenuate as they propagate. If the distance between inputs is L, the number of inputs is N, and the attenuation length is l_(at), then the propagation distance is

L _(tot) =NL  (9)

and let the minimum amplitude needed to be detected is a quarter of the average output amplitude

$\begin{matrix} {A_{m\; i\; n} = {\frac{A_{i\; n}}{4}{{\exp \left( {- \frac{L_{tot}}{l_{at}}} \right)}.}}} & (10) \end{matrix}$

If the group velocity of the spin waves is τ=L_(tot)/C_(sw), then the time needed for one holographic imaging is

τ=NL/c _(sw).  (11)

Assuming that the detection occurs by the inverse of the ME effect, and that its coefficients are the same as for the direct ME effect, we obtain that the connection between the magnetization amplitude and the amplitude of the generated electric field

$\begin{matrix} {\alpha \approx {\frac{ɛ_{p\; z}ɛ_{0}E_{m\; i\; n}}{\Delta \; M}.}} & (12) \end{matrix}$

Thus the minimum output voltage is

$\begin{matrix} {V_{m\; i\; n} = {{E_{m\; i\; n}t_{pz}} = {\frac{\alpha \; M_{s}A_{m\; i\; n}t_{pz}}{ɛ_{pz}ɛ_{0}}.}}} & (13) \end{matrix}$

Combining expressions (10) and (13), we have the following for voltages

$\begin{matrix} {V_{m\; i\; n} = {\frac{V_{i\; n}}{4}{\exp \left( {- \frac{NL}{l_{at}}} \right)}{\frac{\alpha_{2}}{ɛ_{pz}ɛ_{0}\mu_{0}}.}}} & (14) \end{matrix}$

Then the total driving power for N inputs is

$\begin{matrix} {{P_{tot} = {\frac{{NV}_{i\; n}^{2}}{2R} = {\frac{8{NV}_{m\; i\; n}^{2}}{R}{\exp \left( \frac{2{NL}}{l_{at}} \right)}\frac{ɛ_{pz}^{2}}{c^{4}\alpha^{4}}}}},} & (15) \end{matrix}$

where C is the speed of light. For minimum detectability, the output voltage should exceed the Johnson noise voltage by 5×. The spectral density of noise is

V _(n) ^(l)=4k _(B) TR.  (16)

The required power within the bandwidth B (approximately equal to the ac voltage frequency) is

$\begin{matrix} {P_{tot} = {800{NBk}_{B}T\; {\exp \left( \frac{2{NL}}{l_{at}} \right)}{\frac{ɛ_{pz}^{2}}{c^{4}\alpha^{4}}.}}} & (17) \end{matrix}$

And the total energy for one imaging is

E _(wt) =P _(wt)τ.  (18)

Using the magnetostriction parameters for the most advantageous case of Terfenol-D and PMN-PT, the magnetoelectric coefficient

α=57 ns/m≈17/c.  (19)

The dielectric constant of PMN-PT is now ∈_(pz)=100 Substituting the parameters of the holographic system: N=32, L=60 nm, C_(sw)=4000 m/s, B=100 GHz, l_(at)=24 μm, we obtain:

τ=480 ps, P_(tot)=150 μW, E_(tot)=72 fJ.

While a number of advantages of embodiments described herein are listed above, the list is not exhaustive. Other advantages of embodiments described above will be apparent to one of ordinary skill in the art, having read the present disclosure. Although specific embodiments have been illustrated and described herein, it will be appreciated by those of ordinary skill in the art that any arrangement which is calculated to achieve the same purpose may be substituted for the specific embodiment shown. This application is intended to cover any adaptations or variations of the present invention. It is to be understood that the above description is intended to be illustrative, and not restrictive. Combinations of the above embodiments, and other embodiments will be apparent to those of skill in the art upon reviewing the above description. The scope of the invention includes any other applications in which the above structures and fabrication methods are used. The scope of the invention should be determined with reference to the appended claims, along with the full scope of equivalents to which such claims are entitled. 

What is claimed is:
 1. A memory device, comprising: an array of intersecting magnetic wave guides; a number of magnets located at junctions of the intersecting magnetic wave guides; and spin wave generator/detectors located at a periphery of the array and coupled to the intersecting magnetic wave guides. 